A room has the shape of a right circular cylinder with radius r = 10ft
abnd height h = 8ft. A spider is on the room's ceiling , 7 feet from and
directly to the east of the ceiling's center. A fly on the room's floor,
7 feet from and directly to the west of the floor's center. Determine (analytically
or numerically) the minimum distance the spider would have tyo crawl in
order to reach the fly.
If the fly is 7 feet from the center then he is only 3 feet from the
edge of the floor and similarly the spider is only 3 feet from the edge
of the ceiling. Now if we can determine the shortest route for the spider
to travel around the cylinder we will have the problem solved.
To do this we look at the surface area of the cyllinder. The surface area
of a circular cylinder is simply a rectangular region with height of 8 and
width equal to the cicumference of the ceiling.
The shortest distance from the east side of the ceiling to the west side
of the floor is the line that follows the path of the diagonal of the rectangular
region. Therefore, if the spider travels the path along the radius to the
edge, then follows the path of the diagonal of the region, and simply follows
the path of the radius that the fly is sitting on , it will have crawled
the shortest possible distance.